Nonlinear Process Monitoring Using Kernel Nonnegative Matrix Factorization

This paper focuses on developing an advanced nonlinear process monitoring technique involving fault detection and identification methods. The new monitoring methods are proposed based on two nonlinear matrix factorization algorithms. Both factorizations use the kernel method to replace lower-dimensional nonlinearity using higher-dimensional linearity by nonlinearly mapping the data onto a high-dimensional linear space. In the high-dimensional linear space, also known as feature space, the first factorization decomposes the data matrix into two low-rank matrix products, in which the first matrix factor is restricted to being orthogonal and non-negative leading to a good performance in the subspace approximation of the original data. In the second factorization, a matrix consisting of all types of fault samples is decomposed into two low-rank matrix products, in which the second matrix factor is restricted to being orthogonal and non-negative providing a clear K-means clustering interpretation. On the basis of the above two factorizations, the corresponding fault detection and identification methods are developed. Finally, the proposed approaches are used to monitor the penicillin fermentation process (PFP), and encouraging experimental results are achieved.